No it wouldn't, for software to be "Free software" it must be GPL-or-other-copyleft-license licensed, which aside from being trivially impossible in a world without intellectual property laws, also has different outcomes than placing the source in the public domain. For example nothing prevents me from taking some public domain code and including it in my closed-source application, but the GPL forbids this.

No, for free software to be "Free Software" it must respect the Four Freedoms (https://www.gnu.org/philosophy/free-sw.en.html). GPL-or-other-copyleft-license happens to respect them, but so do the Apache, BSDs, MIT and other licenses which are not copyleft.

Note: "Copyleft" as opposed to simply Free Software entails reciprocity, e.g., the "viral" part of the GPL. See https://en.wikipedia.org/wiki/Copyleft

In a world without intellectual property, your closed-source application would be a trade secret that would quickly get out.